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In the paper, we concentrate on the map $x\mapsto x^{\frac{p^n+1}{2}}$ on$\mathbb{F}_{p^n}$ and using combinatorial and number theory techniques, wecompute its detailed $c$-differential spectrum for all values of $c\neq 1$ (thespectrum for $c=1$ is known).

The $c$-differential spectrum of $x\mapsto x^{\frac{p^n+1}{2}}$ in finite fields of odd characteristics